To do so, half of the towel should be behind the blade, and the other half should be in front of it.

To do so, I have created one "addition" mask on the blade. I then copied the layer containing the addition mask and paste it.
On the paste layer, I changed the mask from addition to "subtraction". The shape and movement of both masks are thus exactly the same.

Here are pictures of the addition and subtraction masks.

But there's a problem. On AE composition and on the rendered video, I get this black line around the blade.

In my case I had an effect on the video or photo layer and when I tried to mask out a section it left a thin dark line around parts of the mask. I fixed this by pre composing the video with all attributes included, then applied the mask to the pre-comp.